

A144521


Tetrahedral numbers k*(k+1)*(k+2)/6 such that exactly one of k, k+1, and k+2 is prime.


1



0, 20, 56, 84, 165, 220, 364, 455, 680, 816, 1140, 1330, 1771, 2024, 2300, 3654, 4060, 4960, 5456, 7770, 8436, 9139, 10660, 11480, 13244, 14190, 16215, 17296, 18424, 23426, 24804, 26235, 32509, 34220, 37820, 39711, 47905, 50116, 52394, 57155
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..40.


EXAMPLE

k=0: Of the three numbers (0,1,2), exactly one is prime, so 0*1*2/6 = 0 is in the sequence.
k=1: Of the three numbers (1,2,3), exactly two are prime, so 1*2*3/6 = 1 is not in the sequence.
k=4: Of the three numbers (4,5,6), exactly one is prime, so 4*5*6/6 = 20 is in the sequence.


MAPLE

isPr := proc(n) if isprime(n) then 1; else 0; end if; end proc: for n from 0 to 300 do if isPr(n)+isPr(n+1)+isPr(n+2) = 1 then printf("%d, ", n*(n+1)*(n+2)/6 ) ; end if; end do: # R. J. Mathar, May 01 2010


CROSSREFS

Cf. A000040, A000392, A141468, A152622, A152916.
Sequence in context: A108108 A316935 A123456 * A044122 A044503 A109806
Adjacent sequences: A144518 A144519 A144520 * A144522 A144523 A144524


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Dec 15 2008


EXTENSIONS

Corrected (455, 14190, 17296 inserted, 16560 removed etc.) by R. J. Mathar, May 01 2010
Name and Example section clarified by Jon E. Schoenfield, Aug 06 2017


STATUS

approved



